Quantum Entanglement in Corpuses of Documents

Abstract

We show that data collected from corpuses of documents violate the Clauser-Horne-Shimony-Holt version of Bell's inequality (CHSH inequality) and therefore indicate the presence of quantum entanglement in their structure. We obtain this result by considering two concepts and their combination and coincidence operations consisting of searches of co-occurrences of exemplars of these concepts in specific corpuses of documents. Measuring the frequencies of these co-occurrences and calculating the relative frequencies as approximate probabilities entering in the CHSH inequality, we obtain manifest violations of the latter for all considered corpuses of documents. In comparing these violations with those analogously obtained in an earlier work for the same combined concepts in psychological coincidence experiments with human participants, also violating the CHSH inequality, we identify the entanglement as being carried by the meaning connection between the two considered concepts within the combination they form. We explain the stronger violation for the corpuses of documents, as compared to the violation in the psychology experiments, as being due to the superior meaning domain of the human mind and, on the other side, to the latter reaching a broader domain of meaning and being possibly also actively influenced during the experimentation. We mention some of the issues to be analyzed in future work such as the violations of the CHSH inequality being larger than the 'Cirel'son bound' for all of the considered corpuses of documents.

Quantum Structure in Cognition: Human Language as a Boson Gas of Entangled Words

“…This means that the interactions between 'words', which are the boson particles of language in our description, is mainly one of 'quantum superposition' and 'quantum entanglement', or more precisely one of 'overlapping de Broglie wave functions'. This corresponds well with some of our earlier findings, when studying the combinations of concepts in human language, namely that superposition and entanglement are abundant, and the type of entanglement is deep, namely it also violates additionally to Bell's inequality the marginal laws (Aerts, 2009b;Aerts, Broekaert & Gabora, 2011;Aerts & Sozzo, 2011Aerts, Sozzo & Veloz, 2015aAerts et al, 2012Aerts et al, , 2018aAerts et al, ,b,c, 2019aAerts Arguëlles, 2018;Beltran & Geriente, 2019).…”

Are Words the Quanta of Human Language? Extending the Domain of Quantum Cognition

“…Two studies in Table 2 can be classified in the field of Natural Language Processing. In these studies, we used the corpora of documents ‘Google Books’ and ‘COCA’, and the analogous probabilities, needed to fill in the terms of the Clauser–Horne–Shimony–Holt inequality, were calculated for these studies using the relative frequencies of texts found in the respective corpora of documents [ 31 ]. We have named these studies ‘The Google Books Natural Language Processing Study’ and ‘The COCA Natural Language Processing Study’ in Table 2 .…”

“…In Section 4 we introduce the ‘von Neumann entropy’ in human human language and show how it is greater than zero for single words while the entropy of the total text is zero, thus demonstrating the subadditivity of entropy in human language, very analogous to what takes place for quantum entities. To this end, we use the data from five studies of combinations of words that violate Bell’s inequalities [ 27 ] from previous works by our Brussels research group over the last decade [ 28 , 29 , 30 , 31 ]. This illustrates the second of our new insights, namely that in human language, a text telling a story possesses a lower entropy than each of its words.…”

How images combine meaning: quantum entanglement in visual perception

“…Among the quantum effects recently identified within the quantum cognition research program (Aerts 2009;Aerts et al 2013aAerts et al , b, 2018Busemeyer and Bruza 2012;Dalla Chiara et al 2015a, b;Khrennikov 2010;Melucci 2015), quantum entanglement is certainly one of the most important and intriguing ones, with the additional advantage that its quantum fingerprint can directly be tested experimentally (Aerts and Sozzo 2011;Bruza et al 2009Bruza et al , 2015Gronchi and Strambini 2017;Beltran and Geriente 2019).…”

“…Our research team provided additional evidence of entanglement in concept combination in 2018, when we discovered that the CHSH inequality is also violated in a Web test where the exemplars of The Animal Acts are 'chosen' in document retrieval operations using specific corpuses of documents, like 'Google Books' (Beltran and Geriente 2019). Also here, however, an unanticipated result was attained: the CHSH inequality is violated by an amount that exceeds the famous 'Cirel'son bound' for genuinely quantum violations (Cirel'son 1980)-for example, the CHSH factor is equal to 3.4058, definitely higher than the bound of 2 √ 2 = 2.8284 predicted by quantum theory for entangled states and product measurements.…”